Mass concentration for the $L^2$-critical Nonlinear Schrödinger equations of higher orders

Chae, Myeongju; Hong, Sunggeum; Lee, Sanghyuk

Mass concentration for the $L^2$-critical Nonlinear Schrödinger equations of higher orders

Authors

Chae, Myeongju

Hong, Sunggeum

Lee, Sanghyuk

Description

We consider the mass concentration phenomenon for the $L^2$-critical nonlinear Schrödinger equations of higher orders. We show that any solution $u$ to $iu_{t} + (-Δ)^{\fracα2} u =\pm |u|^\frac{2α}{d}u$, $u(0,\cdot)\in L^2$ for $α>2$, which blows up in a finite time, satisfies a mass concentration phenomenon near the blow-up time. We verify that as $α$ increases, the size of region capturing a mass concentration gets wider due to the stronger dispersive effect.
21 pages, 2 figures